Fidelity for kicked atoms with gravity near a quantum resonance

TL;DR

This paper investigates the stability of kicked atoms under gravity near quantum resonance, revealing how fidelity decay relates to arithmetic properties of gravity and tunneling from stable islands, using a pseudo-classical approximation.

Contribution

It introduces a pseudo-classical approach to analyze fidelity decay in kicked atoms near quantum resonance, linking decay behavior to arithmetic properties of gravity.

Findings

Fidelity behavior depends on gravity's arithmetic properties near resonance.

Long-time fidelity decay is due to tunneling from stable islands.

A simple ansatz effectively models the fidelity decay observed in simulations.

Abstract

Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultra cold atoms. The parametric stability of the quantum dynamics is studied using the fidelity. In the case of a quantum resonance, it is shown that the behavior of the fidelity depends on arithmetic properties of the gravity parameter. Close to a quantum resonance, the long time asymptotics of the fidelity is studied by means of a {\em pseudo-classical} approximation first introduced by Fishman {\em et al.} [J. Stat. Phys. {\bf 110}, 911 (2003)]. The long-time decay of fidelity arises from the tunneling out of pseudo-classical stable islands, and a simple ansatz is proposed which satisfactorily reproduces the main features observed in numerical simulations.